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Abstract

There is described in the present paper a method, discovered empirically, for computing the approximate number of “least perceptible differences” between any two colors of the same brightness whose specifications are available. This method has been stated in simple form as an empirical relation; it is shown to be in substantial agreement with extant sensibility data of the following types: (1) the least wave-length difference perceptible in the pure spectrum as a function of wave length (Steindler, Jones); (2) the least dominant-wave-length difference perceptible at constant purity as a function of purity (Watson, Tyndall); (3) the least purity difference perceptible at constant dominant wave length as a function of purity (Donath); (4) the least purity difference perceptible near zero purity as a function of dominant wave length (Priest, Brickwedde), and (5) the least color-temperature difference perceptible as a function of color temperature (Priest). A mixture diagram is included showing colors specified by their trilinear coordinates and by the dominant wave length and purity of their stimuli. From this diagram the number of “least perceptible differences” separating any two colors of the same brightness may be read with a degree of certainty indicated by the comparisons here presented.

The empirical relation was originally expressed in terms of distribution (“sensation,” “excitation”) curves which suggest a three-components theory of vision (Young-Helmholtz); but it has been re-expressed in terms of curves which suggest an opponent-colors theory (Hering). Since this re-expression is nearly as convenient as the original expression, it is concluded that such success as has been demonstrated for the empirical relation can not be used as an argument for either form of theory; rather is a theory suggested which is more complex than either, such as that of G. E. Müller.

Comparison of the subjective mean determined by Jacobsohn’s experimental method with the saturation mean from relation (1a).

Size of interval between the colors of the components in LPDs† 100|r1−r2|

Difference between saturation mean and the experimental subjective mean in LPDs† 100|
r¯-r¯¯e|

Jacobsohn 360P

Küchler 360P

rj

rk

Mean
rj+rk2=r¯e

1

360

0

0.700

0.333

0.516

125.4

157.8

0.456

0.488

0.472

36.7

4.4

2

360

90

.700

.421

.560

213.5

205.4

.545

.537

.541

27.9

1.9

3

360

180

.700

.511

.606

270.7

275.8

.605

.610

.608

18.9

0.2

4

360

270

.700

.604

.652

310.3

327.4

.646

.665

.656

9.6

0.4

* By relation (1a) the r-coordinate of the saturation mean is merely the arithmetical mean of the r-coordinates, hence:
r¯=(r1+r2)/2.† To give the color interval in classical “least perceptible differences” (LPDs), K of relation (1a) is taken as 1/100 (see Table 2).

Size of interval between the colors of the components in LPDs† 100|r1−r2|

Difference between saturation mean and the experimental subjective mean in LPDs† 100|
r¯-r¯¯e|

Jacobsohn 360P

Küchler 360P

rj

rk

Mean
rj+rk2=r¯e

1

360

0

0.700

0.333

0.516

125.4

157.8

0.456

0.488

0.472

36.7

4.4

2

360

90

.700

.421

.560

213.5

205.4

.545

.537

.541

27.9

1.9

3

360

180

.700

.511

.606

270.7

275.8

.605

.610

.608

18.9

0.2

4

360

270

.700

.604

.652

310.3

327.4

.646

.665

.656

9.6

0.4

* By relation (1a) the r-coordinate of the saturation mean is merely the arithmetical mean of the r-coordinates, hence:
r¯=(r1+r2)/2.† To give the color interval in classical “least perceptible differences” (LPDs), K of relation (1a) is taken as 1/100 (see Table 2).